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Role of Bi-Directional Migration in Two Similar Types of Ecosystems

Author

Listed:
  • Nikhil Pal

    (Department of Mathematics, Visva-Bharati University, Santiniketan 731235, India)

  • Sudip Samanta

    (Department of Mathematics, Faculty of Science & Arts-Rabigh, King Abdulaziz University, Rabigh 25732, Saudi Arabia)

  • Maia Martcheva

    (Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
    Work supported by NSF grant DMS-1515661.)

  • Joydev Chattopadhyay

    (Agricultural and Ecological Research Unit, Indian Statistical Institute 203, B. T. Road, Kolkata 700108, India)

Abstract

Migration is a key ecological process that enables connections between spatially separated populations. Previous studies have indicated that migration can stabilize chaotic ecosystems. However, the role of migration for two similar types of ecosystems, one chaotic and the other stable, has not yet been studied properly. In the present paper, we investigate the stability of ecological systems that are spatially separated but connected through migration. We consider two similar types of ecosystems that are coupled through migration, where one system shows chaotic dynamics, and other shows stable dynamics. We also note that the direction of the migration is bi-directional and is regulated by the population densities. We propose and analyze the coupled system. We also apply our proposed scheme to three different models. Our results suggest that bi-directional migration makes the coupled system more regular. We have performed numerical simulations to illustrate the dynamics of the coupled systems.

Suggested Citation

  • Nikhil Pal & Sudip Samanta & Maia Martcheva & Joydev Chattopadhyay, 2018. "Role of Bi-Directional Migration in Two Similar Types of Ecosystems," Mathematics, MDPI, vol. 6(3), pages 1-16, March.
  • Handle: RePEc:gam:jmathe:v:6:y:2018:i:3:p:36-:d:134423
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    References listed on IDEAS

    as
    1. Pal, Nikhil & Samanta, Sudip & Chattopadhyay, Joydev, 2014. "Revisited Hastings and Powell model with omnivory and predator switching," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 58-73.
    2. Upadhyay, Ranjit Kumar & Rai, Vikas, 2009. "Complex dynamics and synchronization in two non-identical chaotic ecological systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2233-2241.
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    Cited by:

    1. de Godoy, Isabelle Bueno Silva & McGrane-Corrigan, Blake & Mason, Oliver & Moral, Rafael de Andrade & Godoy, Wesley Augusto Conde, 2023. "Plant-host shift, spatial persistence, and the viability of an invasive insect population," Ecological Modelling, Elsevier, vol. 475(C).

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